| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +17 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
y \left (-1\right ) &= 2 \\
y^{\prime }\left (-1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \begin{align*}
y^{\prime \prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
m y^{\prime \prime }+k y&=0 \\
y \left (0\right ) &= a \\
y^{\prime }\left (0\right ) &= b \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=3+4 \sin \left (2 t \right ) \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 1.059 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=t^{2} {\mathrm e}^{3 t}+6 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+y&=t^{2}+3 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
y^{\prime \prime }+y&=3 \sin \left (2 t \right )+\cos \left (2 t \right ) t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
u^{\prime \prime }+w_{0}^{2} u&=\cos \left (t w \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+4 y&=2 \sinh \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\cosh \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.479 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t^{2}+3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t +4 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \sin \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
y^{\prime \prime }+y&=t \left (1+\sin \left (t \right )\right ) \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.475 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.147 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=2 t^{2}+4 \,{\mathrm e}^{2 t} t +t \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-4 y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}+2 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.687 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=2 \cos \left (t w \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t w \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }+y&=3 \cos \left (t w \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (\frac {t}{4}\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.558 |
|
| \begin{align*}
y^{\prime \prime }+y+\frac {y^{3}}{5}&=\cos \left (t w \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.392 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (t w \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.351 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \csc \left (\frac {t}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
4 y^{\prime \prime }+y&=2 \sec \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=g \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.564 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.888 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=3 x^{{3}/{2}} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.661 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=g \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.004 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 0.799 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=4 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.287 |
|
| \begin{align*}
y^{\prime \prime }+y&=g \left (t \right ) \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.188 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.191 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.098 |
|
| \begin{align*}
6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{t} t^{2}+7 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=\cos \left (2 t \right ) t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 9 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
y \left (0\right ) &= 9 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.578 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.090 |
|